A remark to a multipoint boundary value problem
A remark to one result of M. E. Muldoon
A remark to the Floquet theorem for systems of linear differential equations
A remarkable periodic solution of the three-body problem in the case of equal masses.
A representation theorem for the linear quasi-differential equation .
A resonance problem for nonlinear Duffing equation
A result concerning meromorphic solutions in the unit disk of algebraic differential equations
A resummed branching process representation for a class of nonlinear ODEs.
A reversed Poincaré inequality for monotone functions.
A review of the matrix Riccati equation
A Riccati technique for proving oscillation of a half-linear equation.
A rigidity phenomenon for the Hardy-Littlewood maximal function
The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as those nonconstant...
A Role of Abel's Equation in the Stabitity Theory of Differential Equations
A role of the coefficient of the differential term in qualitative theory of half-linear equations
The aim of this contribution is to study the role of the coefficient in the qualitative theory of the equation , where with . We discuss sign and smoothness conditions posed on , (non)availability of some transformations, and mainly we show how the behavior of , along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati...
A sampling theorem associated with boundary-value problems with not necessarily simple eigenvalues.
A Schur method for the solution of the matrix Riccati equation.
A second look at the first result of Landesman-Lazer type.
A second order ODE with a nonlinear final condition.
A second order SDE for the Langevin process reflected at a completely inelastic boundary
It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.
A second-order boundary value problem with nonlinear and mixed boundary conditions: existence, uniqueness, and approximation.